A review on contact Hamiltonian and Lagrangian systems

Abstract

Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great effort to study this type of dynamics both in theoretical aspects and in its potential applications in geometric mechanics and mathematical physics. This paper is intended to be a review of some of the results that the authors and their collaborators have recently obtained on the subject.

arXiv admin note: text overlap with arXiv:1911.05409, arXiv:1904.11429

References in corpus (1)

• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$

Cited by in corpus (8)

• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Contact Lagrangian systems subject to impulsive constraints
• Nonsmooth Herglotz variational principle
• An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications
• Generalized virial theorem for contact Hamiltonian systems
• A review on coisotropic reduction in Symplectic, Cosymplectic, Contact and Co-contact Hamiltonian systems
• A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
• On Geometrical Couplings of Dissipation and Curl Forces